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I am trying to reconstruct the tuning of the Roman water-organ (hydraulis) of Aquincum. The original instrument had 13 pipes for each of the 4 registers (three stopped pipe registers and one open pipe register), and it was possible to play one, two, three, or all four pipes corresponding to each key at the same time.

The best description I found of what could be the tuning comes from the booklet of "Apollo & Dionysus" cd (https://www.chandos.net/chanimages/Booklets/DC4188.pdf), which is based on an actual hydraulis reconstruction by Justus Willberg:

The organ is tuned to an ancient tonal system, drawing upon a range of sources, including Bellermann and Koine Hormasia (Codex Palatinus 281, et al.). The registers are assigned individual modes (Hyperlydian, Hyperiastian, Lydian and Phrygian), allowing a specific set of notes to be played in each register: proslambanómenos, hypáte hypaton, parypáte hypaton, diápemptos, hypáte, parypáte, khromatiké, diátonos, mése, parámesos, tríte, paranéte, néte. In today’s notation this corresponds approximately to the pitch series D E F G A B♭ B C' D' E' F' G' A'. The organ can also be played with all the registers switched on, which results in a characteristic timbre in which the open Hyperlydian register dominates.

What I understand with my limited musical knowledge is:

  1. the register of the open pipes (which should be the highest pitched one) was Hyperlydian;
  2. the three registers of the stopped pipes were Hyperiastian, Lydian and Phrygian;
  3. one of the registers (the highest one?) was tuned according to the scale (that I do not recognize) D E F G A B♭ B C' D' E' F' G' A'.

My question is: how was this organ tuned? What were the pitches for each register? It seems they could be played at the same time, but would they sound nice together?


Edit:
As suggested by user Owain Evans, this is the instrument:

However, it can't be the setup presented in Hagel's book since (1) Hagels himself doubts the correctness of Walker-Mayer reconstruction and (2) none of the registers in Hagel's picture (borrowed from Walker-Mayer, actually) has the range proposed by Willberg

The supposed range of the Aquincum organ from HAGEL, S. (2018). Ancient Greek music: a new technical history. Cambridge, Cambridge University Press, p365.

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    Maybe The Roman organ of Aquincum archive.org/embed/romanorganofaqui0000walc (need to register on archive.org). Has 119 pages, quite alot of images, tuning from a brief glance.
    – user70304
    Jul 25 '20 at 11:58
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    Thanks, I did not know it was accessible. However, recent scholarship (Ancient Greek Music by Hagel) seems to reject the musical reconstruction by Walcker-Mayer as wrong Jul 25 '20 at 12:17
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    It’s in German, but here’s a site about a reconstruction done in the 1990s: hydraulis.de/0496e29a0c08d0302/index.html Also I learned today that pairs of aulos were often stopped (with wax or metal slides) to two different (but related) diatonic modes for a single performance. That caused the burden of the performer having to be careful about certain note combinations, but also allowed flexibility in key and harmony. It could be similar with the hydraulis. Jul 26 '20 at 5:50
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    NB: “Iastian” is another name for “Ionian”, so hyperiastian is just hyperionian. I think the alleged “modern scale” mentioned from D to A’ including a Bb should be temporarily ignored in favor of researching the ancient pitches corresponding to the modes named for each register. It does seem like the modes mentioned in facts 1 and 2 are listed in order from highest register to lowest, but of course there is much overlap (that part of the diagram at the bottom of the question seems somewhat accurate). Jul 26 '20 at 6:51
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    Warning :-) -- in the absence of some physical evidence (dug up an ancient set of pipes) or specified pipe lengths & diameters in units we trust, the best you can do is tune the correct intervals, not the exact pitches . As you no doubt know, in just the last few centuries, middle "A" has moved by at least 10% Jul 28 '20 at 13:59

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